To access to the terrains that may be soft and hard, even and uneven, a novel robot (NEZA-I) with the self-adaptive mobile mechanism has been developed. Its mobile mechanism consists of two symmetric transformable wheel-track (TWT) units. Each TWT unit is driven by only one servo motor, and can efficiently move over rough terrains by changing the locomotion mode or by transforming the track configuration. It has the self-adaptability to the irregular environment. This paper introduces briefly the structure of NEZA-I, and presents the drive system and its self-adaptive principle of the mobile mechanism. The drive ratios of the drive system are estimated. Finally, basic experiments verify the mobility of NEZA-I, and prove the feasibility of the concept of self-adaptive mobile mechanism. Based on the theory of mechanisms, it can provide an idea for the study on the self-adaptive control to the robot.